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作者：Bayraktar, Erhan; Zhang, Yuchong
作者单位：University of Michigan System; University of Michigan; University of Toronto
摘要：We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrodinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players' welfare as ...
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作者：Amiet, Ben; Collevecchio, Andrea; Scarsini, Marco; Zhong, Ziwen
作者单位：Monash University; Luiss Guido Carli University
摘要：In finite games, mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large number of players can each choose one of two possible strategies and the payoffs are independent and identically distributed with the possibility of ties. We provide asymptotic results about the random number of pure Nash equilibria, such as fast growth an...
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作者：Filmus, Yuval; Kawase, Yasushi; Kobayashi, Yusuke; Yamaguchi, Yutaro
作者单位：Technion Israel Institute of Technology; University of Tokyo; Kyoto University; Kyushu University; Kyushu University
摘要：A set function is called XOS if it can be represented by the maximum of additive functions. When such a representation is fixed, the number of additive functions required to define the XOS function is called the width. In this paper, we study the problem of maximizing XOS functions in the value oracle model. The problem is trivial for the XOS functions of width 1 because they are just additive, but it is already nontrivial even when the width is restricted to 2. We show two types of tight boun...
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作者：Peck, James; Rampal, Jeevant
作者单位：University System of Ohio; Ohio State University; Indian Institute of Management (IIM System); Indian Institute of Management Ahmedabad
摘要：This paper analyzes a monopoly firm's profit-maximizing mechanism in the following context. There is a continuum of consumers with a unit demand for a good. The distribution of the consumers' valuations is given by one of two possible demand distributions/states. The consumers are uncertain about the demand state, and they update their beliefs after observing their own valuation for the good. The firm is uncertain about the demand state but infers it from the consumers' reported valuations. Th...
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作者：Grishchenko, Dmitry; Iutzeler, Franck; Malick, Jerome
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
摘要：Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient method harnessing this underlying structure. We introduce two key components: (i) a random subspace proximal gradient algorithm; and (ii) an identification-based sampling of the subspaces. Their interplay brings a significant performance improvement on typical ...
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作者：Fu, Guanxing; Graewe, Paulwin; Horst, Ulrich; Popier, Alexandre
作者单位：Hong Kong Polytechnic University; Deloitte Touche Tohmatsu Limited; Humboldt University of Berlin; Humboldt University of Berlin; Le Mans Universite
摘要：We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with a finite terminal value yet a singular driver. Extending the method of continuation to linear-quadratic FBSDEs with a singular driver, we prove that the M...
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作者：Correa, Jose; Foncea, Patricio; Hoeksma, Ruben; Oosterwijk, Tim; Vredeveld, Tjark
作者单位：Universidad de Chile; Massachusetts Institute of Technology (MIT); University of Twente; Maastricht University
摘要：The classic prophet inequality states that, when faced with a finite sequence of nonnegative independent random variables, a gambler who knows the distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work, we consider the situation in which the sequence comes in random order. We look at both a nonadaptive and an adaptive version of ...
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作者：Evren, Ozgur; Husseinov, Farhad
作者单位：New Economic School; Ministry of Education of Azerbaijan Republic; ADA University
摘要：Consider a dominance relation (a preorder) >= on a topological space X, such as the greater than or equal to relation on a function space or a stochastic dominance relation on a space of probability measures. Given a compact set K subset of X, we study when a continuous real function on K that is strictly monotonic with respect to >= can be extended to X without violating the continuity and monotonicity conditions. We show that such extensions exist for translation invariant dominance relation...
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作者：Liu, Peng; Schied, Alexander; Wang, Ruodu
作者单位：University of Essex; University of Waterloo
摘要：In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool in decision theory. As our main results, we characterize distributional transforms satisfying various properties, and this includes an equivalent set of conditions which forces a distributional transfo...
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作者：Burke, James, V; Tim, Hoheisel; Nguyen, Quang, V
作者单位：University of Washington; University of Washington Seattle; McGill University
摘要：In this paper, we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone convexity, is straightforward. The results are established under a verifiable Slater-type condition, with relaxed monotonicity and without lower semi continuity assumptions on the functions in play. The versatility of our findings is illustrated by a series of applications in optimization and matrix analys...
